/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 75 Factor completely, or state that... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 75

Factor completely, or state that the polynomial is prime. $$x^{3}-4 x$$

Short Answer

Expert verified
The factored form of the polynomial \(x^{3}-4x\) is \(x(x+2)(x-2)\).

Step by step solution

01

Searching for the greatest common factor

The given polynomial is \(x^{3}-4x\). Start by identifying the common factors. We can see that 'x' can be factored out from all the terms of the expression.
02

Factoring out the common factor

By factoring the common factor 'x' out of each term, the given polynomial is rewritten as \(x(x^{2}-4)\).
03

Recognizing difference of squares

The expression inside the brackets, \(x^{2}-4\), is a difference of squares which can further be factored. A difference of squares is an expression of the form \(a^{2}-b^{2}\), and it can be factored into \((a+b)(a-b)\).
04

Factoring the difference of squares

Factoring the expression \(x^{2}-4\) using the formula for difference of squares, it becomes \((x+2)(x-2)\).
05

Final factored form of the polynomial

Combining all the factored expressions together, the final factored form of the polynomial \(x^{3}-4x\) is \(x(x+2)(x-2)\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}-6 x+3, \text { for } x=7$$

Find the intersection of the sets. $$\\{0,1,3,5\\} \cap\\{-5,-3,-1\\}$$

$$\text { factor completely.}$$ $$x^{2 n}+6 x^{n}+8$$

Determine whether each statement in Exercises 43鈥�50 is true or false. $$0 \geq-13$$

Rewrite each expression without absolute value bars. $$|300|$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.